Tables of Sample Sizes for Two GroupsTables of Sample Sizes for Multiple (>2) GroupsReferences

These tables provides sample sizes (per group) needed to compare the means of 2
groups, assuming that the data is normally distributed, that the variance
in the groups are similar, and that the sample sizes for the groups are the same
- Power = 1-β
- α = Probability of Type I Error
- es = Effect size = difference between means / population of within group Standard Deviation

Effect Size 0.05→1.00Effect Size 1.05→2.00Effect Size 2.05→3.00

Power

0.8

0.9

0.95

Alpha

0.1

0.05

0.01

0.001

0.1

0.05

0.01

0.001

0.1

0.05

0.01

0.001

es

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

0.05

3607

4947

4947

6281

8031

9345

12370

13663

5256

6852

6852

8407

10415

11905

15293

16726

6852

8659

8659

10397

12618

14253

17940

19490

0.1

902

1238

1238

1571

2009

2338

3095

3418

1315

1714

1714

2103

2605

2978

3825

4184

1714

2166

2166

2600

3156

3565

4487

4875

0.15

402

551

551

699

894

1040

1377

1521

585

762

762

935

1159

1325

1702

1861

762

963

963

1157

1404

1586

1996

2168

0.2

226

310

310

394

504

586

776

857

329

429

429

527

653

746

959

1048

429

542

542

651

790

893

1124

1221

0.25

145

199

199

253

323

376

498

550

211

275

275

338

418

478

614

672

275

347

347

417

507

572

720

783

0.3

101

139

139

176

225

262

346

383

147

191

191

235

291

333

428

468

191

242

242

290

352

398

501

544

0.35

75

102

102

130

166

193

255

282

108

141

141

173

214

245

315

344

141

178

178

214

259

293

369

401

0.4

57

78

78

100

127

148

196

217

83

108

108

133

165

188

242

265

108

136

136

164

199

225

283

308

0.45

45

62

62

79

101

118

156

172

66

86

86

105

130

149

192

210

85

108

108

130

158

178

224

244

0.5

37

51

51

64

82

96

127

140

53

70

70

86

106

121

156

170

69

88

88

105

128

145

182

198

0.55

31

42

42

53

68

79

105

116

44

58

58

71

88

101

129

141

58

73

73

87

106

120

151

164

0.6

26

36

36

45

58

67

89

98

37

49

49

60

74

85

109

119

48

61

61

74

89

101

127

139

0.65

22

30

30

39

49

57

76

84

32

42

42

51

63

73

93

102

41

52

52

63

77

86

109

119

0.7

19

26

26

33

43

50

66

73

28

36

36

44

55

63

81

89

36

45

45

54

66

75

94

103

0.75

17

23

23

29

38

44

58

64

24

32

32

39

48

55

71

78

31

40

40

48

58

65

83

90

0.8

15

20

20

26

33

39

51

57

21

28

28

34

43

49

63

69

28

35

35

42

51

58

73

79

0.85

13

18

18

23

30

34

46

50

19

25

25

31

38

43

56

61

25

31

31

37

46

51

65

71

0.9

12

16

16

21

27

31

41

45

17

22

22

27

34

39

50

55

22

28

28

34

41

46

58

63

0.95

11

15

15

19

24

28

37

41

15

20

20

25

31

35

45

50

20

25

25

30

37

42

53

57

1

10

14

14

17

22

26

34

37

14

18

18

22

28

32

41

45

18

23

23

27

33

38

48

52

Power

0.8

0.9

0.95

Alpha

0.1

0.05

0.01

0.001

0.1

0.05

0.01

0.001

0.1

0.05

0.01

0.001

es

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1.05

9

12

12

16

20

23

31

34

13

17

17

21

25

29

38

41

16

21

21

25

30

34

44

47

1.1

8

11

11

14

18

21

28

31

12

15

15

19

23

27

34

38

15

19

19

23

28

32

40

43

1.15

8

11

11

13

17

20

26

29

11

14

14

17

22

25

32

35

14

18

18

21

26

29

37

40

1.2

7

10

10

12

16

18

24

27

10

13

13

16

20

23

29

32

13

16

16

20

24

27

34

37

1.25

7

9

9

12

15

17

23

25

9

12

12

15

19

21

27

30

12

15

15

18

22

25

32

34

1.3

6

8

8

11

14

16

21

23

9

11

11

14

17

20

26

28

11

14

14

17

21

23

29

32

1.35

6

8

8

10

13

15

20

22

8

11

11

13

16

18

24

26

10

13

13

16

19

22

27

30

1.4

6

7

7

9

12

14

19

21

8

10

10

12

15

17

22

25

10

12

12

15

18

20

26

28

1.45

5

7

7

9

11

13

18

19

7

9

9

11

14

16

21

23

9

11

11

14

17

19

24

26

1.5

5

7

7

8

11

13

17

18

7

9

9

11

13

15

20

22

9

11

11

13

16

18

23

25

1.55

5

6

6

8

10

12

16

17

6

8

8

10

13

15

19

21

8

10

10

12

15

17

22

23

1.6

6

6

8

10

11

15

17

6

8

8

10

12

14

18

20

8

10

10

12

14

16

20

22

1.65

6

6

7

9

11

14

16

6

7

7

9

11

13

17

19

7

9

9

11

13

15

19

21

1.7

5

5

7

9

10

14

15

5

7

7

9

11

12

16

18

7

9

9

10

13

14

18

20

1.75

5

5

7

8

10

13

14

5

7

7

8

10

12

15

17

7

8

8

10

12

14

18

19

1.8

5

5

6

8

9

12

14

5

6

6

8

10

11

15

16

6

8

8

9

12

13

17

18

1.85

5

5

6

8

9

12

13

5

6

6

8

9

11

14

15

6

8

8

9

11

13

16

17

1.9

5

5

6

7

9

11

13

5

6

6

7

9

10

13

15

6

7

7

9

11

12

15

17

1.95

6

7

8

11

12

6

6

7

9

10

13

14

5

7

7

8

10

12

15

16

2

5

7

8

11

12

5

5

7

8

10

12

14

5

7

7

8

10

11

14

15

Power

0.8

0.9

0.95

Alpha

0.1

0.05

0.01

0.001

0.1

0.05

0.01

0.001

0.1

0.05

0.01

0.001

es

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

1 tail

2 tail

2.05

5

7

8

10

11

5

5

6

8

9

12

13

5

6

6

8

9

11

14

15

2.1

5

6

7

10

11

5

5

6

8

9

12

13

5

6

6

7

9

10

13

14

2.15

5

6

7

10

11

5

5

6

7

9

11

12

5

6

6

7

9

10

13

14

2.2

5

6

7

9

10

5

5

6

7

8

11

12

6

6

7

8

10

12

13

2.25

5

6

7

9

10

5

5

6

7

8

10

11

5

5

7

8

9

12

13

2.3

6

7

9

10

5

7

8

10

11

5

5

6

8

9

11

12

2.35

5

6

8

9

5

7

8

10

11

5

5

6

8

9

11

12

2.4

5

6

8

9

5

6

7

10

10

5

5

6

7

8

11

12

2.45

5

6

8

9

5

6

7

9

10

5

5

6

7

8

10

11

2.5

5

6

8

9

5

6

7

9

10

5

5

6

7

8

10

11

2.55

5

6

8

8

5

6

7

9

10

5

5

5

7

8

10

11

2.6

5

6

7

8

5

6

7

9

9

5

7

7

10

10

2.65

5

5

7

8

6

6

8

9

5

6

7

9

10

2.7

5

5

7

8

5

6

8

9

5

6

7

9

10

2.75

5

5

7

8

5

6

8

9

5

6

7

9

10

2.8

5

7

8

5

6

8

9

5

6

7

9

9

2.85

5

7

7

5

6

8

8

5

6

7

8

9

2.9

5

7

7

5

6

7

8

5

6

6

8

9

2.95

5

6

7

5

6

7

8

5

6

8

9

3

5

6

7

5

5

7

8

5

6

8

9

ExplanationGroups=3,4Groups=5,6Groups=7,8Groups=9,10Groups=11,12

Because of the large sizes, the tables are placed in their own panels. Click on the appropriate tab to see the table

Each table contains sample sizes for combinations of

k : The number of groups in the analysis of variance (3 to 12), in different tables

Combination of α and Power in the columns

α : Probability of Type I Error, values of 0.1, 0.05, 0.01

Power (1-β) : β being probability of Type II Error, values of 0.8, 0.9, and 0.95

Effect size in d and f in rows

d : Effect Size = Maximum difference between any two groups / within group Standard Deviation

f : 3 models of Cohen's Effect Size

f1 : Model 1 : where differences between groups are generally smaller than the maximum difference